Threefold extremal contractions of type (IA)
Mori, Shigefumi ; Prokhorov, Yuri
Kyoto J. Math., Tome 51 (2011) no. 1, p. 393-438 / Harvested from Project Euclid
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Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f:(X,C)\to (Z,o)$ such that $C=f^{-1}(o)_{\operatorname {red}}$ and $-K_{X}$ is ample. Assume that a general member $F\in |-K_{X}|$ meets $C$ only at one point $P$ , and furthermore assume that $(F,P)$ is Du Val of type A if index $(X,P)=4$ . We classify all such germs in terms of a general member $H\in |\mathscr {O}_{X}|$ containing $C$ .
Publié le : 2011-05-15
Classification:  14J30,  14E,  14E30 
@article{1303494508,
     author = {Mori, Shigefumi and Prokhorov, Yuri},
     title = {Threefold extremal contractions of type (IA)},
     journal = {Kyoto J. Math.},
     volume = {51},
     number = {1},
     year = {2011},
     pages = { 393-438},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303494508}
}

Mori, Shigefumi; Prokhorov, Yuri. Threefold extremal contractions of type (IA). Kyoto J. Math., Tome 51 (2011) no. 1, pp.  393-438. http://gdmltest.u-ga.fr/item/1303494508/